{"id":764,"date":"2020-10-27T09:15:52","date_gmt":"2020-10-27T08:15:52","guid":{"rendered":"https:\/\/marieleapouliquen.com\/?p=764"},"modified":"2025-10-27T10:32:49","modified_gmt":"2025-10-27T09:32:49","slug":"modele-1-les-planetes-boucle-dor","status":"publish","type":"post","link":"https:\/\/marieleapouliquen.com\/?p=764","title":{"rendered":"Mod\u00e8le 1 : Les plan\u00e8tes Boucle d&rsquo;Or"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"764\" class=\"elementor elementor-764\">\n\t\t\t\t<div class=\"elementor-element elementor-element-bc52d44 e-flex e-con-boxed wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"bc52d44\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ea864a1 elementor-widget elementor-widget-html\" data-id=\"ea864a1\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<!-- ================ PAGE : \u00c9QUILIBRE RADIATIF \u2013 JEU PLAN\u00c8TES ================ -->\n<style>\n  :root{\n    --wrap: 1100px; --gap: 22px;\n    --bg:#ffffff; --ink:#111827; --muted:#374151;\n    --card:#c0f0e0; --line:#c0f0e0; --accent:#0ea5e9; --accent-ink:#fff;\n  }\n  @media (prefers-color-scheme: dark){\n    :root{\n      --bg:#053e2b; --ink:#053e2b; --muted:#374151;\n      --card:#ffffff; --line:#E8D9FC; --accent:#053e2b; --accent-ink:#fff;\n    }\n  }\n  body{background:var(--bg); color:var(--ink);}\n  .wrap{max-width:var(--wrap); margin:0 auto; padding:clamp(12px,2vw,24px);}\n\n  \/* HERO *\/\n   .hero{\n      background:\n        radial-gradient(800px 400px at -10% -20%, rgba(255,215,64,.85) 0%, rgba(255,215,64,0) 60%),\n        linear-gradient(105deg, #ffb703 0%, #fd7e14 22%, #7b2cbf 60%, #0a2540 100%);\n      border:0; border-radius:20px;\n      padding:clamp(22px,3vw,36px); margin-bottom:var(--gap);}\n  .hero h1{margin:0 0 6px; font-size:clamp(30px,4vw,30px); line-height:1.15;color:#fff;}\n  .hero p{margin:0; color:var(--muted); font-size:clamp(15px,2.1vw,17px); color:#fff; text-shadow:0 2px 4px rgba(0,0,0,.4) }\n  .cta{display:flex; gap:12px; flex-wrap:wrap; margin-top:14px;}\n  .btn{display:inline-block; padding:10px 14px; border-radius:12px; text-decoration:none;\n       font-weight:700; border:1px solid var(--line);}\n  .btn.primary{background:#2D2868; color:#fff; border-color:transparent;}\n  .btn.ghost{color:#2D2868; background:#F6F0FE;border-color:transparent;}\n\n  section{margin: clamp(28px,4vw,48px) 0;}\n  .module{background:var(--card); border:1px solid var(--line); border-radius:16px; padding:clamp(14px,2vw,20px);}\n  .module h2{margin:0 0 6px;}\n  .caption{font-size:14px; color:var(--muted); margin:6px 0 12px;}\n\n  \/* Colonnes explications *\/\n  .cols{display:grid; gap:var(--gap); grid-template-columns: 2fr 1fr;}\n  @media(max-width:1000px){ .cols{grid-template-columns:1fr;} }\n  .card{background:var(--card); border:1px solid var(--line); border-radius:14px; padding:18px;}\n  .card h3{margin:0 0 8px;}\n  .muted{color:var(--muted);}\n  .sep{height:1px; background:var(--line); margin:18px 0;}\n  .list{list-style:disc; padding-left:20px; margin:8px 0 0;}\n  .note{font-style: italic; margin-top:6px; color:var(--muted);}\n\n  \/* Styles internes du jeu (onglets\/contr\u00f4les) \u2013 gard\u00e9s simples *\/\n  .game-wrap{max-width: 1100px; margin: 0 auto;}\n  .tabs{ display:flex; gap:8px; flex-wrap:wrap; margin-bottom: 12px; }\n  .tabbtn{ cursor:pointer; border:1px solid var(--line); padding:8px 12px; border-radius:10px; background:#f7f7f7; }\n  .tabbtn.active{ background:#111; color:#fff; border-color:#111; }\n  .panel{ display:none; }\n  .panel.active{ display:block; }\n  .controls{ display:grid; grid-template-columns: 1fr 1fr; gap:16px; align-items:center; margin-bottom: 10px; }\n  .controls .row{ display:grid; grid-template-columns: 180px 1fr 120px; align-items:center; gap:10px; }\n  .controls .row input[type=\"number\"]{ width: 100%; padding:8px 10px; border:1px solid #cbd5e1; border-radius:10px; }\n  .controls .row input[type=\"range\"]{ width: 100%; }\n  .controls .row label{ font-weight: 600; }\n  .bar{ height:1px; background:#e6e6e6; margin: 12px 0; }\n  .right{ text-align:right; }\n  .btn.small{ padding:6px 10px; border-radius:10px; }\n  select#sel-planet{ padding:8px 12px; font-size:16px; min-width: 300px; border:1px solid #cbd5e1; border-radius:10px; font-weight:600; }\n  @media (max-width: 760px){ .controls{ grid-template-columns: 1fr; } }\n<\/style>\n\n<div class=\"wrap\">\n\n  <!-- HERO -->\n  <div class=\"hero\">\n    <h1>\ud83c\udf0e\ud83d\udfe0 Les Plan\u00e8tes Boucle d\u2019Or <\/h1>\n    <p>Pourquoi certaines plan\u00e8tes sont-elles glac\u00e9es, d\u2019autres br\u00fblantes tandis que la Terre est juste \u00e0 la bonne temp\u00e9rature pour permettre la co-existence des trois \u00e9tats de l'eau&nbsp;?  \n       Ce mini-jeu vous invite \u00e0 explorer la relation entre l\u2019\u00e9nergie re\u00e7ue du Soleil et la temp\u00e9rature de surface des plan\u00e8tes.<\/p>\n    <div class=\"cta\">\n      <a href=\"#jeu\" class=\"btn primary\">Lancer le jeu<\/a>\n      <a href=\"#explications\" class=\"btn ghost\">Lire les explications<\/a>\n    <\/div>\n  <\/div>\n\n  <!-- MODULE : JEU -->\n  <section id=\"jeu\">\n    <div class=\"module\">\n      <h2>Simulateur interactif<\/h2>\n      <p class=\"caption\"> Ce mini-jeu explore comment la <strong>distance au Soleil<\/strong> et <strong>l\u2019alb\u00e9do<\/strong> (part de lumi\u00e8re r\u00e9fl\u00e9chie) influencent la temp\u00e9rature d\u2019une plan\u00e8te. En ajustant ces param\u00e8tres, vous calculez la <strong>temp\u00e9rature d\u2019\u00e9quilibre radiatif<\/strong> \u2014 celle d\u2019une plan\u00e8te \u201cnue\u201d, sans atmosph\u00e8re ni effet de serre.<\/p>\n    <p class=\"caption\"> Le mod\u00e8le reste volontairement simple&nbsp;: il n\u2019englobe pas toute la complexit\u00e9 des climats plan\u00e9taires, mais il met en lumi\u00e8re un m\u00e9canisme fondamental&nbsp;: l\u2019\u00e9quilibre entre l\u2019\u00e9nergie re\u00e7ue du Soleil et l\u2019\u00e9nergie r\u00e9\u00e9mise vers l\u2019espace. Comparez ensuite les valeurs calcul\u00e9es aux <strong>temp\u00e9ratures observ\u00e9es<\/strong> pour comprendre pourquoi certaines plan\u00e8tes (comme <em>V\u00e9nus<\/em> ou <em>la Terre<\/em>) sont plus chaudes qu\u2019un corps noir id\u00e9al. <\/p>\n   <p class=\"caption\"> \ud83d\udca1 Indice : plus l\u2019alb\u00e9do est \u00e9lev\u00e9, plus la plan\u00e8te renvoie la lumi\u00e8re \u2014 et plus elle reste froide. <\/p>\n\n      <!-- ======= JEU PLOTLY (ton code d\u2019origine) ======= -->\n      <div class=\"game-wrap\">\n        <div class=\"tabs\">\n          <button class=\"tabbtn active\" data-target=\"#p-obs\">Temp\u00e9rature r\u00e9elle de surface<\/button>\n          <button class=\"tabbtn\" data-target=\"#p-energy\">\u00c9nergie solaire re\u00e7ue<\/button>\n          <button class=\"tabbtn\" data-target=\"#p-model\">\u00c9quilibre interactif<\/button>\n          <button class=\"tabbtn\" data-target=\"#p-compare\">Temp\u00e9rature r\u00e9elle vs Temp\u00e9rature mod\u00e9lis\u00e9e<\/button>\n        <\/div>\n\n        <!-- 1) Observ\u00e9 -->\n        <div class=\"panel active\" id=\"p-obs\"><div id=\"chart-obs\"><\/div><\/div>\n\n        <!-- 2) \u00c9nergie -->\n        <div class=\"panel\" id=\"p-energy\"><div id=\"chart-energy\"><\/div><\/div>\n\n        <!-- 3) Mod\u00e8le (contr\u00f4les + \u00e9volution temporelle) -->\n        <div class=\"panel\" id=\"p-model\">\n          <div class=\"controls\" aria-label=\"Contr\u00f4les du mod\u00e8le\">\n            <div class=\"row\" style=\"grid-column: 1 \/ -1;\">\n              <label for=\"sel-planet\">Plan\u00e8te<\/label>\n              <select id=\"sel-planet\">\n                <option>Mercure<\/option><option>V\u00e9nus<\/option><option>Terre<\/option><option>Mars<\/option>\n                <option>Jupiter<\/option><option>Saturne<\/option><option>Uranus<\/option><option>Neptune<\/option>\n              <\/select>\n              <div class=\"right\">\n                <button id=\"btn-reset\" class=\"btn small\" title=\"R\u00e9initialiser les valeurs de la plan\u00e8te\">\u21ba R\u00e9initialiser<\/button>\n              <\/div>\n            <\/div>\n\n            <div class=\"row\">\n              <label for=\"range-albedo\">Alb\u00e9do (0\u20130,9)<\/label>\n              <input id=\"range-albedo\" type=\"range\" min=\"0\" max=\"0.9\" step=\"0.01\" \/>\n              <input id=\"num-albedo\" type=\"number\" min=\"0\" max=\"0.9\" step=\"0.01\" \/>\n            <\/div>\n\n            <div class=\"row\">\n              <label for=\"range-L\">Irradiance L (W\/m\u00b2)<\/label>\n              <input id=\"range-L\" type=\"range\" min=\"0.5\" max=\"20000\" step=\"0.1\" \/>\n              <input id=\"num-L\" type=\"number\" min=\"0.5\" max=\"20000\" step=\"0.1\" \/>\n            <\/div>\n          <\/div>\n\n          <div id=\"chart-model\"><\/div>\n          <div class=\"bar\"><\/div>\n          <div class=\"note\">\u00c9volution temporelle (relaxation vers l\u2019\u00e9quilibre) \u2014 synchronis\u00e9e avec la plan\u00e8te et les param\u00e8tres ci-dessus.<\/div>\n          <div class=\"checks\" aria-label=\"Afficher\/masquer les courbes de r\u00e9f\u00e9rence\" style=\"display:flex;gap:16px;flex-wrap:wrap;margin:8px 0 12px;\">\n            <label><input type=\"checkbox\" id=\"chk-v\" checked> V\u00e9nus<\/label>\n            <label><input type=\"checkbox\" id=\"chk-e\" checked> Terre<\/label>\n            <label><input type=\"checkbox\" id=\"chk-m\" checked> Mars<\/label>\n          <\/div>\n          <div id=\"chart-time-embed\"><\/div>\n        <\/div>\n\n        <!-- 4) Comparaison -->\n        <div class=\"panel\" id=\"p-compare\">\n          <div id=\"chart-compare\"><\/div>\n          <div class=\"note\">\u25c9 Ronds pleins : T_observ\u00e9e &nbsp;&nbsp; \u25cb Ronds clairs : T_calcul\u00e9e (mod\u00e8le)<\/div>\n        <\/div>\n      <\/div>\n      <!-- ======= \/JEU PLOTLY ======= -->\n    <\/div>\n  <\/section>\n\n  <!-- EXPLICATIONS -->\n  <section id=\"explications\">\n    <div class=\"cols\">\n      <div class=\"card\">\n\n        <h3>Le mod\u00e8le de l\u2019\u00e9quilibre radiatif<\/h3>\n        <p class=\"muted\">Pour illustrer la relation entre l\u2019\u00e9nergie solaire re\u00e7ue par une plan\u00e8te et sa temp\u00e9rature de surface, nous avons construit un mod\u00e8le de <strong>temp\u00e9rature d\u2019\u00e9quilibre radiatif<\/strong>, fond\u00e9 sur l\u2019hypoth\u00e8se du <em>corps noir<\/em> : chaque plan\u00e8te est suppos\u00e9e absorber et r\u00e9-\u00e9mettre l\u2019\u00e9nergie solaire sans atmosph\u00e8re ni transfert interne de chaleur. Ce mod\u00e8le calcule la temp\u00e9rature d\u2019une plan\u00e8te \u00ab nue \u00bb, d\u00e9termin\u00e9e par l\u2019\u00e9nergie re\u00e7ue et son <strong>alb\u00e9do<\/strong> (fraction de lumi\u00e8re r\u00e9fl\u00e9chie).<\/p>\n        <div class=\"sep\"><\/div>\n\n        <h3>Visualisation<\/h3>\n        <ul class=\"list\">\n          <li><strong>(1) Temp\u00e9rature r\u00e9elle de surface<\/strong> : temp\u00e9rature moyenne de surface observ\u00e9e pour chaque plan\u00e8te.<\/li>\n          <li><strong>(2) \u00c9nergie solaire re\u00e7ue<\/strong> : puissance du rayonnement en fonction de la distance au Soleil (elle chute rapidement avec la distance).<\/li>\n          <li><strong>(3) \u00c9quilibre interactif<\/strong> : jouez sur l\u2019alb\u00e9do et l\u2019irradiance pour ajuster la temp\u00e9rature d'\u00e9quilibre radiatif.<\/li>\n          <li><strong>(4) Temp\u00e9rature r\u00e9elle vs Temp\u00e9rature mod\u00e9lis\u00e9e<\/strong> : comparez la temp\u00e9rature calcul\u00e9e par le mod\u00e8le avec la temp\u00e9rature r\u00e9elle de surface.<\/li>\n        <\/ul>\n        <div class=\"sep\"><\/div>\n\n        <h3>Pourquoi la temp\u00e9rature d\u2019\u00e9quilibre radiatif est-elle plus basse que la temp\u00e9rature r\u00e9elle&nbsp;?<\/h3>\n        <p class=\"muted\">\n        Lorsque la temp\u00e9rature observ\u00e9e d\u00e9passe la temp\u00e9rature d\u2019\u00e9quilibre radiatif, cela signifie que la plan\u00e8te conserve ou g\u00e9n\u00e8re davantage de chaleur qu\u2019un simple <em>corps noir<\/em>.  \n        Chez les <strong>plan\u00e8tes telluriques<\/strong> (comme la Terre ou V\u00e9nus), cette diff\u00e9rence provient principalement des <strong>gaz \u00e0 effet de serre<\/strong>, qui pi\u00e8gent une partie du rayonnement infrarouge.  \n        Pour les <strong>plan\u00e8tes g\u00e9antes<\/strong> (Jupiter, Saturne, Neptune), c\u2019est surtout la <strong>chaleur interne<\/strong> \u2014 r\u00e9sidu de leur formation et compression gravitationnelle \u2014 qui explique leur temp\u00e9rature plus \u00e9lev\u00e9e.  \n        Le <em>flux g\u00e9othermique<\/em>, quant \u00e0 lui, reste tr\u00e8s faible pour les plan\u00e8tes rocheuses&nbsp;: il est n\u00e9gligeable face au rayonnement solaire re\u00e7u.\n        <\/p>\n      <\/div>\n\n      <aside class=\"card\">\n         <h3>\u00c0 exp\u00e9rimenter<\/h3>\n        <ul class=\"list\" style=\"list-style:disc; padding-left:20px;\">\n          <li>Faites varier la <strong>distance au Soleil<\/strong> (irradiance L) et observez comment la temp\u00e9rature r\u00e9agit.<\/li>\n          <li>Augmentez l\u2019<strong>alb\u00e9do<\/strong> pour voir comment la plan\u00e8te se refroidit en r\u00e9fl\u00e9chissant davantage de lumi\u00e8re.<\/li>\n          <li>Comparez l\u2019\u00e9cart entre la <strong>temp\u00e9rature r\u00e9elle<\/strong> et la <strong>temp\u00e9rature mod\u00e9lis\u00e9e<\/strong> pour V\u00e9nus (fort effet de serre) et Mars (atmosph\u00e8re tr\u00e8s fine).<\/li>\n        <\/ul>\n      <\/aside>\n    <\/div>\n  <\/section>\n\n<\/div>\n\n<!-- Charge Plotly (retirez si d\u00e9j\u00e0 pr\u00e9sent sur la page) -->\n<script src=\"https:\/\/cdn.plot.ly\/plotly-2.35.2.min.js\"><\/script>\n\n<script>\n\/* ========= Ton code de jeu (inchang\u00e9 dans la logique) ========= *\/\n(function(){\n  \/\/ --- Donn\u00e9es de base ---\n  const name   = ['Mercure','V\u00e9nus','Terre','Mars','Jupiter','Saturne','Uranus','Neptune'];\n  const d      = [57.9,108.2,149.2,287.9,778.5,1434,2871,4495]; \/\/ millions de km\n  const L0     = [12300,3140,1360,600,50,10,3.5,1.5];            \/\/ W\/m\u00b2 (valeurs fournies)\n  const albedo0= [0.06,0.7,0.3,0.15,0.42,0.45,0.53,0.66];\n  const temp_true = [179,462,15,-63,-163,-189,-220,-218];        \/\/ \u00b0C\n  const color  = ['gold','fuchsia','lightblue','red','peru','burlywood','turquoise','mediumpurple'];\n\n  \/\/ Copiables\n  let L = [...L0];\n  let albedo = [...albedo0];\n\n  \/\/ Mod\u00e8le plan\u00e8te nue (\u00b0C)\n  const sigma = 5.67e-8; \/\/ W\/m\u00b2\/K^4\n  function nakedplanet(alpha, L){\n    return Math.pow(L*(1-alpha)\/(4*sigma), 0.25) - 273.15;\n  }\n  function computeTempModel(){ return albedo.map((a,i)=>nakedplanet(a, L[i])); }\n\n  \/\/ Int\u00e9gration temporelle (type nakedplanet1)\n  function integrateTemps(alpha, Lin){\n    const dt_year = 1; \/\/ an\n    const depth = 4000; \/\/ m\n    const Cp = depth * 4.2e6; \/\/ J K^-1 m^-2\n    const steps = 2000;\n    const heatIn = Lin * (1 - alpha) \/ 4; \/\/ W\/m\u00b2\n    let T = 0; \/\/ K\n    let HC = Cp * T; \/\/ J\/m\u00b2\n    const time = new Array(steps);\n    const tempC = new Array(steps);\n    for (let i=0;i<steps;i++){\n      const heatOut = sigma * Math.pow(T,4);\n      HC += (heatIn - heatOut) * dt_year * 3.14e7; \/\/ s\/an\n      T = HC \/ Cp;\n      time[i] = i * dt_year;\n      tempC[i] = T - 273.15;\n    }\n    return {time, tempC};\n  }\n\n  \/\/ === Graphiques ===\n  \/\/ 1) Observ\u00e9\n  Plotly.newPlot('chart-obs', [{\n    x: d, y: temp_true, text: name, mode: 'markers+text', textposition: 'top center',\n    marker: { size: 10, color }, type: 'scatter',\n    hovertemplate: '<b>%{text}<\/b><br>Distance: %{x:.1f} Mkm<br>T\u00b0 observ\u00e9e: %{y:.0f} \u00b0C<extra><\/extra>'\n  }], {\n    title: 'Temp\u00e9ratures de surface (observ\u00e9es)',\n    xaxis: { title: 'Distance au Soleil (millions de km)', range:[0,5000] },\n    yaxis:{ title:'Temp\u00e9rature [\u00b0C]' },\n    margin:{ t:50, r:20, b:60, l:60 }\n  }, {responsive:true, displayModeBar:false});\n\n  \/\/ 2) \u00c9nergie re\u00e7ue\n  Plotly.newPlot('chart-energy', [{\n    x: d, y: L, text: name, mode: 'markers+text', textposition: 'top center',\n    marker: { size: 10, color }, type: 'scatter',\n    hovertemplate: '<b>%{text}<\/b><br>Distance: %{x:.1f} Mkm<br>\u00c9nergie: %{y:.0f} W\/m\u00b2<extra><\/extra>'\n  }], {\n    title: '\u00c9nergie solaire re\u00e7ue',\n    xaxis: { title: 'Distance au Soleil (millions de km)', range:[0,5000] },\n    yaxis:{ title:'\u00c9nergie [W\/m\u00b2]' },\n    margin:{ t:50, r:20, b:60, l:60 }\n  }, {responsive:true, displayModeBar:false});\n\n  \/\/ 3) Mod\u00e8le\n  let temp_model = computeTempModel();\n  Plotly.newPlot('chart-model', [{\n    x: d, y: temp_model, text: name, mode: 'markers+text', textposition: 'top center',\n    marker: { size: 10, color }, type: 'scatter',\n    hovertemplate: '<b>%{text}<\/b><br>Distance: %{x:.1f} Mkm<br>T\u00b0 calcul\u00e9e: %{y:.0f} \u00b0C<extra><\/extra>'\n  }], {\n    title: 'Temp\u00e9ratures d\\'\u00e9quilibre radiatif',\n    xaxis: { title: 'Distance au Soleil (millions de km)', range:[0,5000] },\n    yaxis:{ title:'Temp\u00e9rature [\u00b0C]' },\n    margin:{ t:50, r:20, b:60, l:60 }\n  }, {responsive:true, displayModeBar:false});\n\n  \/\/ 4) Comparaison\n  const traceReal = { name:'Observ\u00e9e', x:d, y:temp_true, text:name, mode:'markers+text', textposition:'top center', marker:{ size:10, color }, type:'scatter', hovertemplate:'<b>%{text}<\/b><br>Distance: %{x:.1f} Mkm<br>T\u00b0 observ\u00e9e: %{y:.0f} \u00b0C<extra><\/extra>' };\n  const traceModel = { name:'Calcul\u00e9e', x:d, y:temp_model, text:name, mode:'markers', marker:{ size:12, color, line:{color, width:2}, symbol:'circle-open', opacity:1 }, type:'scatter', hovertemplate:'<b>%{text}<\/b><br>Distance: %{x:.1f} Mkm<br>T\u00b0 calcul\u00e9e: %{y:.0f} \u00b0C<extra><\/extra>' };\n  Plotly.newPlot('chart-compare', [traceReal, traceModel], {\n    title:'R\u00e9el vs Mod\u00e8le',\n    xaxis:{ title:'Distance au Soleil (millions de km)', range:[0,5000] },\n    yaxis:{ title:'Temp\u00e9rature [\u00b0C]' },\n    margin:{ t:50, r:20, b:60, l:60 }, legend:{ orientation:'h', x:0, y:1.12 }\n  }, {responsive:true, displayModeBar:false});\n\n  \/\/ --- Contr\u00f4les (onglet Mod\u00e8le) ---\n  const sel = document.getElementById('sel-planet');\n  const rA = document.getElementById('range-albedo');\n  const nA = document.getElementById('num-albedo');\n  const rL = document.getElementById('range-L');\n  const nL = document.getElementById('num-L');\n  const btnReset = document.getElementById('btn-reset');\n\n  function syncInputs(){\n    const i = sel.selectedIndex;\n    rA.value = albedo[i]; nA.value = albedo[i];\n    rL.value = L[i];      nL.value = L[i];\n    const S = integrateTemps(albedo[i], L[i]);\n    Plotly.restyle('chart-time-embed', { x:[S.time], y:[S.tempC], line:[{color: color[i], width:3}] }, [3]);\n  }\n  function applyChange(){\n    const i = sel.selectedIndex;\n    albedo[i] = Math.max(0, Math.min(0.9, parseFloat(nA.value)));\n    L[i]      = Math.max(0.5, Math.min(20000, parseFloat(nL.value)));\n\n    temp_model = computeTempModel();\n    Plotly.restyle('chart-energy', { y:[L] });\n    Plotly.restyle('chart-model', { y:[temp_model] });\n    Plotly.restyle('chart-compare', { y:[temp_true, temp_model] });\n\n    const S = integrateTemps(albedo[i], L[i]);\n    Plotly.restyle('chart-time-embed', { x:[S.time], y:[S.tempC], line:[{color: color[i], width:3}] }, [3]);\n  }\n\n  rA.addEventListener('input', ()=>{ nA.value = rA.value; applyChange(); });\n  nA.addEventListener('input', ()=>{ rA.value = nA.value; applyChange(); });\n  rL.addEventListener('input', ()=>{ nL.value = rL.value; applyChange(); });\n  nL.addEventListener('input', ()=>{ rL.value = nL.value; applyChange(); });\n  sel.addEventListener('change', syncInputs);\n  btnReset.addEventListener('click', ()=>{\n    const i = sel.selectedIndex;\n    albedo[i] = albedo0[i];\n    L[i] = L0[i];\n    syncInputs(); applyChange();\n  });\n\n  \/\/ === \u00c9volution temporelle EMBED ===\n  const Sel0   = integrateTemps(albedo[0], L[0]);\n  const Merc0  = integrateTemps(albedo0[0], L0[0]);\n  const Venus0 = integrateTemps(albedo0[1], L0[1]);\n  const Earth0 = integrateTemps(albedo0[2], L0[2]);\n  const Mars0  = integrateTemps(albedo0[3], L0[3]);\n  const Jup0   = integrateTemps(albedo0[4], L0[4]);\n  const Sat0   = integrateTemps(albedo0[5], L0[5]);\n  const Ura0   = integrateTemps(albedo0[6], L0[6]);\n  const Nep0   = integrateTemps(albedo0[7], L0[7]);\n\n  const tSemb = { name:'Plan\u00e8te s\u00e9lectionn\u00e9e', x:Sel0.time, y:Sel0.tempC, mode:'lines', line:{width:3, color: color[0]} };\n  const tMerc = { name:'Mercure', x:Merc0.time, y:Merc0.tempC, mode:'lines', line:{width:2, color: color[0]} };\n  const tVemb = { name:'V\u00e9nus', x:Venus0.time, y:Venus0.tempC, mode:'lines', line:{width:2, color: color[1]} };\n  const tEemb = { name:'Terre', x:Earth0.time, y:Earth0.tempC, mode:'lines', line:{width:2, color: color[2]} };\n  const tMemb = { name:'Mars',  x:Mars0.time,  y:Mars0.tempC,  mode:'lines', line:{width:2, color: color[3]} };\n  const tJup  = { name:'Jupiter', x:Jup0.time,  y:Jup0.tempC,  mode:'lines', line:{width:2, color: color[4]} };\n  const tSat  = { name:'Saturne', x:Sat0.time,  y:Sat0.tempC,  mode:'lines', line:{width:2, color: color[5]} };\n  const tUra  = { name:'Uranus',  x:Ura0.time,  y:Ura0.tempC,  mode:'lines', line:{width:2, color: color[6]} };\n  const tNep  = { name:'Neptune', x:Nep0.time,  y:Nep0.tempC,  mode:'lines', line:{width:2, color: color[7]} };\n\n  Plotly.newPlot('chart-time-embed',\n    [tVemb, tEemb, tMemb, tSemb, tMerc, tJup, tSat, tUra, tNep],\n    { title:\"Convergence vers T_rad\", xaxis:{ title:'Temps [ann\u00e9es]' }, yaxis:{ title:'Temp\u00e9rature [\u00b0C]' },\n      margin:{ t:50, r:20, b:60, l:60 }, legend:{orientation:'v'} },\n    {responsive:true, displayModeBar:false}\n  );\n\n  \/\/ Init\n  syncInputs();\n\n  \/\/ Checkboxes visibilit\u00e9 des 3 courbes affich\u00e9es\n  const chkV = document.getElementById('chk-v');\n  const chkE = document.getElementById('chk-e');\n  const chkM = document.getElementById('chk-m');\n  function updateRefVisibility(){\n    Plotly.restyle('chart-time-embed', { visible: [chkV.checked ? true : 'legendonly'] }, [0]);\n    Plotly.restyle('chart-time-embed', { visible: [chkE.checked ? true : 'legendonly'] }, [1]);\n    Plotly.restyle('chart-time-embed', { visible: [chkM.checked ? true : 'legendonly'] }, [2]);\n  }\n  [chkV, chkE, chkM].forEach(el => el.addEventListener('change', updateRefVisibility));\n  updateRefVisibility();\n\n  \/\/ --- Tabs ---\n  const buttons = document.querySelectorAll('.tabbtn');\n  buttons.forEach(btn => btn.addEventListener('click', () => {\n    buttons.forEach(b=>b.classList.remove('active'));\n    document.querySelectorAll('.panel').forEach(p=>p.classList.remove('active'));\n    btn.classList.add('active');\n    document.querySelector(btn.dataset.target).classList.add('active');\n    setTimeout(()=>{\n      ['chart-obs','chart-energy','chart-model','chart-compare','chart-time-embed']\n        .forEach(id=>{ const el=document.getElementById(id); if(el){ Plotly.Plots.resize(el); }});\n    }, 0);\n  }));\n})();\n<\/script>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\ud83c\udf0e\ud83d\udfe0 Les Plan\u00e8tes Boucle d\u2019Or Pourquoi certaines plan\u00e8tes sont-elles glac\u00e9es, d\u2019autres br\u00fblantes tandis que la Terre est juste \u00e0 la bonne temp\u00e9rature pour permettre la co-existence des trois \u00e9tats de l&rsquo;eau&nbsp;? Ce mini-jeu vous invite \u00e0 explorer la relation entre l\u2019\u00e9nergie re\u00e7ue du Soleil et la temp\u00e9rature de surface des plan\u00e8tes. Lancer le jeu Lire les explications Simulateur interactif Ce mini-jeu explore comment la distance au Soleil et l\u2019alb\u00e9do (part de lumi\u00e8re r\u00e9fl\u00e9chie) influencent la temp\u00e9rature d\u2019une plan\u00e8te. En ajustant ces param\u00e8tres, vous calculez la temp\u00e9rature d\u2019\u00e9quilibre radiatif \u2014 celle d\u2019une plan\u00e8te \u201cnue\u201d, sans atmosph\u00e8re ni effet de serre. Le mod\u00e8le reste volontairement simple&nbsp;: il n\u2019englobe pas toute la complexit\u00e9 des climats plan\u00e9taires, mais il met en lumi\u00e8re un m\u00e9canisme fondamental&nbsp;: l\u2019\u00e9quilibre entre l\u2019\u00e9nergie re\u00e7ue du Soleil et l\u2019\u00e9nergie r\u00e9\u00e9mise vers l\u2019espace. Comparez ensuite les valeurs calcul\u00e9es aux temp\u00e9ratures observ\u00e9es pour comprendre pourquoi certaines plan\u00e8tes (comme V\u00e9nus ou la Terre) sont plus chaudes qu\u2019un corps noir id\u00e9al. \ud83d\udca1 Indice : plus l\u2019alb\u00e9do est \u00e9lev\u00e9, plus la plan\u00e8te renvoie la lumi\u00e8re \u2014 et plus elle reste froide. Temp\u00e9rature r\u00e9elle de surface \u00c9nergie solaire re\u00e7ue \u00c9quilibre interactif Temp\u00e9rature r\u00e9elle vs Temp\u00e9rature mod\u00e9lis\u00e9e Plan\u00e8te MercureV\u00e9nusTerreMarsJupiterSaturneUranusNeptune \u21ba R\u00e9initialiser Alb\u00e9do (0\u20130,9) Irradiance L (W\/m\u00b2) \u00c9volution temporelle (relaxation vers l\u2019\u00e9quilibre) \u2014 synchronis\u00e9e avec la plan\u00e8te et les param\u00e8tres ci-dessus. V\u00e9nus Terre Mars \u25c9 Ronds pleins : T_observ\u00e9e &nbsp;&nbsp; \u25cb Ronds clairs : T_calcul\u00e9e (mod\u00e8le) Le mod\u00e8le de l\u2019\u00e9quilibre radiatif Pour illustrer la relation entre l\u2019\u00e9nergie solaire re\u00e7ue par une plan\u00e8te et sa temp\u00e9rature de surface, nous avons construit un mod\u00e8le de temp\u00e9rature d\u2019\u00e9quilibre radiatif, fond\u00e9 sur l\u2019hypoth\u00e8se du corps noir : chaque plan\u00e8te est suppos\u00e9e absorber et r\u00e9-\u00e9mettre l\u2019\u00e9nergie solaire sans atmosph\u00e8re ni transfert interne de chaleur. Ce mod\u00e8le calcule la temp\u00e9rature d\u2019une plan\u00e8te \u00ab nue \u00bb, d\u00e9termin\u00e9e par l\u2019\u00e9nergie re\u00e7ue et son alb\u00e9do (fraction de lumi\u00e8re r\u00e9fl\u00e9chie). Visualisation (1) Temp\u00e9rature r\u00e9elle de surface : temp\u00e9rature moyenne de surface observ\u00e9e pour chaque plan\u00e8te. (2) \u00c9nergie solaire re\u00e7ue : puissance du rayonnement en fonction de la distance au Soleil (elle chute rapidement avec la distance). (3) \u00c9quilibre interactif : jouez sur l\u2019alb\u00e9do et l\u2019irradiance pour ajuster la temp\u00e9rature d&rsquo;\u00e9quilibre radiatif. (4) Temp\u00e9rature r\u00e9elle vs Temp\u00e9rature mod\u00e9lis\u00e9e : comparez la temp\u00e9rature calcul\u00e9e par le mod\u00e8le avec la temp\u00e9rature r\u00e9elle de surface. Pourquoi la temp\u00e9rature d\u2019\u00e9quilibre radiatif est-elle plus basse que la temp\u00e9rature r\u00e9elle&nbsp;? Lorsque la temp\u00e9rature observ\u00e9e d\u00e9passe la temp\u00e9rature d\u2019\u00e9quilibre radiatif, cela signifie que la plan\u00e8te conserve ou g\u00e9n\u00e8re davantage de chaleur qu\u2019un simple corps noir. Chez les plan\u00e8tes telluriques (comme la Terre ou V\u00e9nus), cette diff\u00e9rence provient principalement des gaz \u00e0 effet de serre, qui pi\u00e8gent une partie du rayonnement infrarouge. Pour les plan\u00e8tes g\u00e9antes (Jupiter, Saturne, Neptune), c\u2019est surtout la chaleur interne \u2014 r\u00e9sidu de leur formation et compression gravitationnelle \u2014 qui explique leur temp\u00e9rature plus \u00e9lev\u00e9e. Le flux g\u00e9othermique, quant \u00e0 lui, reste tr\u00e8s faible pour les plan\u00e8tes rocheuses&nbsp;: il est n\u00e9gligeable face au rayonnement solaire re\u00e7u. \u00c0 exp\u00e9rimenter Faites varier la distance au Soleil (irradiance L) et observez comment la temp\u00e9rature r\u00e9agit. Augmentez l\u2019alb\u00e9do pour voir comment la plan\u00e8te se refroidit en r\u00e9fl\u00e9chissant davantage de lumi\u00e8re. Comparez l\u2019\u00e9cart entre la temp\u00e9rature r\u00e9elle et la temp\u00e9rature mod\u00e9lis\u00e9e pour V\u00e9nus (fort effet de serre) et Mars (atmosph\u00e8re tr\u00e8s fine).<\/p>\n","protected":false},"author":1,"featured_media":803,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[11],"tags":[],"class_list":["post-764","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-terraklima","entry","has-media"],"_links":{"self":[{"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=\/wp\/v2\/posts\/764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=764"}],"version-history":[{"count":34,"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=\/wp\/v2\/posts\/764\/revisions"}],"predecessor-version":[{"id":816,"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=\/wp\/v2\/posts\/764\/revisions\/816"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=\/wp\/v2\/media\/803"}],"wp:attachment":[{"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/marieleapouliquen.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}